As I have argued elsewhere, it is very difficult to reconcile the idea that God intentionally designed human beings with the statistical explanations we would expect to see in a completed evolutionary theory. One might respond that our current evolutionary theory is not thus completed, but it would be nice to have a story that would fit even with a future completed theory. I now offer such a solution, albeit one I am not fond of.

Suppose first that God determines (either directly or mediately) every quantum event in the evolutionary history of human beings. Suppose further that physical reality is infinite, either spatially or temporally or in the multiverse way, in such wise that the quantum events in our evolutionary history can be arranged into a fairly natural infinite sequence and given frequentist probabilities

So far this is a simple and quite unoriginal solution. And it is insufficient. A standard problem with frequentist accounts is that they get the order of explanations wrong. It is central to a completed evolutionary story that the probabilistic facts explain the arising of human beings. But if the probabilistic facts are grounded in the sequence of events, as on frequentism they are, then they cannot explain what happens in that sequence of events. Some Humeans are happy to bite the bullet and accept circular explanations here, but I take the objection to be very serious.

However, theistic frequentism has a resource that bare frequentism does not. The theistic frequentist can make probability facts be grounded not in the frequencies of the infinite sequence of events as such, but in God’s intention to produce an infinite sequence of events with such-and-such frequencies and to do so under the description “an infinite sequence of events with such-and-such frequencies.” This requires God to have a reason to produce a sequence of events with such-and-such frequencies as such, but a reason is not hard to find–statistical order is a genuine kind of order and order is valuable.

The theistic frequentist now has much less of a circularity worry. It is not the infinite sequence of events that grounds the probabilities that are, in turn, supposed to explain the events within the evolutionary sequence. Rather, it is God’s intention to produce events with such-and-such frequencies that grounds the probabilities, and the events in the sequence can be non-circularly explained by their having frequencies that God had good reason (say, based on order) to produce.

The resulting statistical explanation of the arising of human beings is incomplete. For God chose the frequencies he did as well as the particular events with the frequencies partly in order to produce human beings. Presumably, the full story about God’s intentions will involve an interplay between considerations about the sorts of beings to produce and considerations about the kinds and frequencies of events by which to produce them. But even though the statistical explanation is incomplete, it is still an explanation. And it should be no part of even a completed evolutionary theory to claim that it provides the whole correct explanatory story, but only that it provides a correct explanatory story.

The general point is that the theist can adopt some Humean-style “explanations” (such as frequentist ones) in such a way that the theistic underpinnings compensate for the explanatory poverty of Humean stories (cf. this).

Final technical remarks on frequentism: As a first approximation, we might use standard infinite-sequence frequentism: chances just are frequencies of events in infinite sequences. But there are technical problems with this, most notably that as De Finetti has noted this in general doesn’t actually satisfy the axioms of probability (see here for loads of criticisms). Fortunately, the main technical problems can be overcome by replacing the standard definition of chances in terms of frequencies with a more complex one. There are also philosophical problems. Let me overcome some of these by saying that I am making no claim that chances or probabilities are the same thing as frequencies. Rather, I adopt a pluralism: anything that satisfies the axioms of probability is a probability. Infinite-sequence frequentist “probabilities”, when defined in the tweaked way satisfy the axioms of probability, and hence really are probabilities. In this way, I escape the standard objection to frequentism that surely single-case chances are possible. For I make no claim that all chances or probabilities are of the frequentist variety.

Final note: I really don’t like the frequentist theory I give in this post.

I confess that I do not understand this: “A standard problem with frequentist accounts is that they get the order of explanations wrong. It is central to a completed evolutionary story that the probabilistic facts explain the arising of human beings. But if the probabilistic facts are grounded in the sequence of events, as on frequentism they are, then they cannot explain what happens in that sequence of events.”

I now wonder if one couldn’t do a similar move with a finite sequence. A finite sequence may have frequencies that will approximate something neat and simple. E.g., you throw a coin a million times and you get 501948 heads. That approximates 1/2, and 1/2 is neat and simple. Well, God could *intend* that the finite sequence approximate 1/2 out of a love of (approximate) elegance and simplicity. If so, then roughly speaking the frequency’s being close to 1/2 will be explanatory (the more precise statement would be that God’s intention that the frequency approximate 1/2 will be explanatory).

Start with the sequence of events. It grounds the probabilistic facts. And past events (or sets thereof) explain future events, such as the appearance of humans. So what’s the problem? (I get the circularity objection, but I don’t get how you got the circularity.)

I think the theist can describe divine creation of humankind without getting into the finer points of what probability means within the context of natural evolution. This can be achieved by pointing out that natural evolution does not say how things happen but only describes a model about how thing could have happened. And then claim that there is an alternative theistic description such that if the theory of natural evolution is true there cannot be any observational facts (including those on which the theory is based) which contradict it.
The way to do this is as follows. One posits that God wants two things. First (for reasons that are irrelevant to our discussion), to create humankind just like we are having the specific cognitive faculties we do, etc. And, second (for reasons that are irrelevant in our discussion), to create a world in which a naturalistic (and thus godless) model exists about how humankind came about. A solution would be the following state of affairs:
1) Us observing physical phenomena which are consistent with a model according to which all (including humankind) came about through an indeterministic mechanism. That is to say a mechanism which blindly evolves through one history out of many possible ones, and where the history we observe around us has no properties which require or even only suggest some supernatural guidance.
2) The history we observe around us came about by God choosing it for actualization.
Given the great success of the physical sciences and specifically of quantum mechanics and of the theory of evolution it is very probable that #1 is a property of the actual world. And given omnipotence and omniscience the creative act described in #2 is entirely consistent with theism. The result then is a state of affairs which satisfies the two things God wants.

Dianelos:
“And then claim that there is an alternative theistic description such that if the theory of natural evolution is true there cannot be any observational facts (including those on which the theory is based) which contradict it.”
Sure, one can do this, but this is tending in the direction of scientific irrealism.

Alex,
Scientific realism comes from reifying physical models which are consistent with the science. In other words scientific realism is the metaphysical assumption that scientific models describe reality. As described above the theist may embrace scientific realism without any problems. God in (2) actualizes into reality the physical model described in (1).
It is highly remarkable that the structure of physical law should be such that it makes space for Godâs general and special providence, as well as for human free will. Which means that the interaction problem disappears. Here, roughly, is the idea:
The claim is that in a dualistic reality it is possible for the conscious dimension to cause events in the physical plane, while all events on that plane remain causally closed. How can that work? I will respond by first presenting two analogies, and then by describing how a theistic version of dualism can work in the actual reality in which we exist.
The first analogy (inspired of course by Platoâs cave) is that of a shadow theater. The shadows we observe are in reality caused by the puppeteers and their instruments; on the other hand the shadows themselves may present a causally closed world. So if we only take into consideration information about the shadows we see (the way scientific naturalists only take into consideration physical phenomena) then we need not assume the existence of the puppeteers and their instruments, and will only discuss the internal logic of the shadow play itself. A second analogy is that of playing a virtual reality computer game. What we observe in this game is caused by the computer hardware running a particular software program, itself caused by programmers having a particular intention. On the other hand the events in the computer game itself may (and indeed typically are) causally closed, and while playing the game one need not assume the existence of its real causes.
Let me now describe a dualistic reality which satisfies theismâs premises as well as scientific realism:
According to quantum mechanics a physical system can evolve in many different ways. Only one of these ways will become actual in the physical reality we actually observe. Let us now consider the entire physical universe at some initial state as such a system. Quantum mechanics describes all possible physical universes that can evolve out of this initial state. Perhaps unbeknownst to many, quantum mechanics allows for the evolution of physical universes that would not be ânaturalisticâ or âcausally closedâ in the sense we use the terms, and indeed would strike one as strongly âsupernaturalisticâ. For example quantum mechanics allows for universes in which some people perform miracles, or where the Statue of Liberty now and then swims around Manhattan, and so on.
Let us now define three properties that a possible universe may have. The N-property characterizes the universes that would appear to be naturalistic and causally closed under any possible scientific test. So the âsupernaturalisticâ universes described above lack the N-property. The G-property characterizes the universes in which Godâs will about physical facts would obtain. For example universes in which humans do not evolve according to Godâs design would lack the G-property. Finally the H-property characterizes the universes in which the will of humans about physical facts would obtain â within the limitations of the N-property. So a universe in which we found ourselves incapable of moving our bodies according to our will (within the limitations of physical law) would lack the H-property. Now there is a huge number of possible universes which possess both the N, G, and H properties, and which therefore comport with the physical laws and facts that science discovers, and also with the traditional theistic story of a creator and interacting God, and also with our own experience of life including free will. God continuously actualizes one of these N-G-H universes by randomly picking one out of them (so that there are many physical events which are random and are not caused either by God or by any other person â a fact that helps one solve the problem from evil).
Here then we have the description of a dualistic reality in which non-physical persons who exist in a separate spiritual realm (such as God and ourselves) freely and massively cause events in the physical universe (via the actualization of future physical facts), while all these events remain causally closed under any possible scientific test.

“on the other hand the shadows themselves may present a causally closed world”
They may present a causally closed world, but there is no causation between the shadows, and so they mis-present a causally closed world. (Unless some Humean theory of causation is true.)

Alex,
âThey may present a causally closed world, but there is no causation between the shadows, and so they mis-present a causally closed world.â
Thatâs exactly the theistic position, isnât it? That metaphysical naturalists mis-represent causation? For example, the naturalistic scientific realist holds that mass actually causes spacetime around it to curve (a curious claim if one thinks of it). On the contrary, the theistic scientific realist holds that it’s ultimately Godâs will which causes spacetime around mass to curve â and call the whole thing general providence.
Now of course both assume that their own view is right. Moreover the naturalist thinks he has a good argument against the theistic position, namely the interaction problem. The naturalist thinks that God acting specially in the worldâs history (for example in the evolution of humankind – which is part of Godâs special providence), as well as humans freely acting on their own purposes, would break the physical closure of the world. My argument shows that thanks to the structure of modern physical law that argument doesnât work.
Thus modern science ends up supporting theism in two ways:
First it removes from the theistic worldview a problem that many people, including some theists, think is serious. So, for example, so-called âcreationistsâ think that since evolutionary theory explains the evolution of humanity without assuming any divine causality, the theory contradicts the theistic premise that God specially designed and made humankind. Thus, they falsely conclude, there must be something wrong with evolutionary theory. Their error is to see a contradiction where none exists. That the theory of evolution presents a physically closed story under any possible scientific test does not entail that God has not specially guided it.
Secondly, it saddles naturalism with a serious problem of its own: Falling for the same kind of mistake the creationist does, the naturalist thinks that human freedom would necessarily break the physical closure of the world, and therefore concludes that our experience of freedom must be some kind of illusion. But given the coherence of the theistic view described above, the naturalist must now recognize that it is only on naturalism that freedom is illusory. And given that freedom represents such a fundamental part of the human condition, the fact that theism makes perfect sense of it whereas naturalism doesnât, is good reason for suspecting that naturalism is false.

“On the contrary, the theistic scientific realist holds that it’s ultimately Godâs will which causes spacetime around mass to curve â and call the whole thing general providence.”
I am OK with the “ultimately”, but I still want the mass to mediately cause spacetime to curve. Otherwise we have occasionalism.

âI am OK with the “ultimately”, but I still want the mass to mediately cause spacetime to curve.â
Perhaps âultimatelyâ and âmediatelyâ are weasel words weâd better do without. When I use a hammer to put a nail into the wall, does it make any sense whatsoever to say that the hammer causes the nail to go into the wall?
âOtherwise we have occasionalism.â
The sound of the word is not attractive, but it seems to me obvious that occasionalism is entailed by theism. Otherwise what is it we mean when we say that God is the metaphysically ultimate? What is it that Jesus in the Gospels means when He says to Pilate that he canât change a hair? Or what is the meaning of John 1:3 â Through Him all things were made; without Him nothing was made that has been made? In conclusion I think the Islamic philosophers had it exactly right. Including when they saw that occasionalism does not entail intelligibility.
Perhaps much of the difficulty with dealing with theism comes from kind of making little discounts, from not contemplating the idea of God in the absolute sense it has. It seems clear to me that the efficient cause of all act that has an efficient cause (which excludes the creative and sovereign act of will itself) is Godâs will. When I, a free creature, by my own sovereign will choose to move my hand, itâs by Godâs grace that it actually moves. All other knowledge about the movement of my hand is the deliverance of pattern recognition.